Not legally, no. However, it is quite likely that you could sneak her by the system--just make sure she picks the tickets up from an automated machine (if she picks them up from an agent, the agent may ask for the AAA card).
Once she has the tickets and boards the train, it's EXTREMELY unlikely (as in, nobody around here has EVER been asked) that she'll be asked by the conductor to show the AAA card. I've traveled many, many segments on Amtrak with my Student Advantage card discount, and I've NEVER been asked to show the card itself. (Conductors simply don't care.)
Not that I'm encouraging you to beat the system...
